Question: Simplify the following expression: $ q = -10 + \dfrac{x - 4}{x - 1} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{x - 1}{x - 1}$ $ \dfrac{-10}{1} \times \dfrac{x - 1}{x - 1} = \dfrac{-10x + 10}{x - 1} $ Therefore $ q = \dfrac{-10x + 10}{x - 1} + \dfrac{x - 4}{x - 1} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-10x + 10 + x - 4}{x - 1} $ $q = \dfrac{-9x + 6}{x - 1}$